Given a set of $k$ vectors of length $n$, $X = [x_1, \dots, x_k]$ and another set of $l$ vectors of length $n$, $Y = [y_1, \dots, y_l]$, I'd like to to compute the inner product of every combination of vectors in $X$ and $Y$. For this, I could write $$ Z = X^H Y $$ if the inner product is Euclidean.
Is there a common notation if the inner product is not Eucledian, but some custom $\langle\cdot,\cdot\rangle$? What is the name of this product?